Several techniques exist for retrieving and studying information about the properties of the Solar atmosphere from the polarization state of spectral lines. These are commonly called spectral diagnostics. Among the current problems to which these are applied, one is to understand the interconnection between the solar magnetic field and chromospheric heating. Non-LTE inversion has so far been the most reliable method for inferring chromospheric magnetic fields from high-resolution spectropolarimetric observations. However, if the magnetic field is sufficiently low that the line is in the weak field regime, the weak field approximation is often used as a complement. The latter allows for rapid analysis of large datasets and can be used to infer the vector components of the magnetic field. The reliability of the approximation in highly dynamic and stratified atmospheres has however not been well studied. The purpose of this project is to study and assess the reliability, the validity conditions, and the origin of possible breakdowns of the weak field approximation. This is done by computing the magnetic field of a model chromosphere, performed with realistic three-dimensional magnetohydrodynamics, from synthetic Ca II 8542 polarization profiles. Real magnetic fields are further on inferred from sunspot and plage observations of the same line with the intention to test the method under observational constraints. Stokes I profiles with peculiar shapes are seen in both sunspots and plage, apart from the common quiet profiles. The effect of two such types on the inferred field is studied more closely in this project; raised core profiles, which exhibit a flat core and are common in plage and in the vicinity of bright points, and umbral flashes, which exhibit core emission and are seen in sunspots. The shape of the former is directly connected to presence of steep vertical temperature gradients arising from chromospheric heating, while that of the latter is due to oscillatory motions of the plasma. The weak field approximation works well for observations with high S/N ratio and where quiet profiles are abundant, such as in sunspots. It is vulnerable in plage regions where there is an abundance of raised core (RC) or umbral flash (UF) profiles which lead to failed estimations. Profiles with low S/N tend to yield failed estimations as well. This is common where there is plage, whereby clusters of failed inversions tend to arise in such regions. The vertical component and inclination are well determined, while the horizontal component and azimuth are less well determined. The approximation works well in general, and allows for a rapid and efficient inference of the magnetic field vector as long as the wavelength range is chosen wisely.